## Contractivity of Linear Fractional Transformations (1998)

Venue: | Third Real Numbers and Computers Conference (RNC3 |

Citations: | 8 - 3 self |

### BibTeX

@INPROCEEDINGS{Heckmann98contractivityof,

author = {Reinhold Heckmann},

title = {Contractivity of Linear Fractional Transformations},

booktitle = {Third Real Numbers and Computers Conference (RNC3},

year = {1998},

pages = {45--59}

}

### OpenURL

### Abstract

One possible approach to exact real arithmetic is to use linear fractional transformations (LFT's) to represent real numbers and computations on real numbers. Recursive expressions built from LFT's are only convergent (i.e., denote a well-defined real number) if the involved LFT's are sufficiently contractive. In this paper, we define a notion of contractivity for LFT's. It is used for convergence theorems and for the analysis and improvement of algorithms for elementary functions. Keywords : Exact Real Arithmetic, Linear Fractional Transformations 1 Introduction Linear Fractional Transformations (LFT's) provide an elegant approach to real number arithmetic [8, 17, 11, 14, 12, 6]. One-dimensional LFT's x 7! ax+c bx+d are used in the representation of real numbers and to implement basic unary functions, while two-dimensional LFT's (x; y) 7! axy+cx+ey+g bxy+dx+fy+h provide binary operations such as addition and multiplication, and can be combined to obtain infinite expression trees ...

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